关于时间慢变的广义Logistic模型的多尺度分析
Multiscale Analysis of a Generalized Logistic Model with Slowly Varying Parameters
摘要: 在广义logistic模型中，有三个参数，分别为R (种群内禀增长率)，K (种群最大容纳量)，β (种群对环境利用程度的参数)。模型中它们通常为常数，但在自然环境中它们都是关于时间缓慢变化的，这时模型的精确解是求不出来的。本文通过使用多尺度的方法求出关于时间慢变模型的渐近解，数值模拟例证了所得渐近解的有效性。
Abstract: In the generalized logistic model, there are three parameters, R (intrinsic rate of growth), K (maxi-mum tolerance of population) and β (the degree of population using environmental resources), which are constants in the model. In fact, they vary slowly with time in the natural environment. It is hard to obtain the exact solution. In this paper we get the asymptotic solution of the model using the method of multi-scale. Numerical simulation illustrates the validity of the asymptotic solution obtained.
文章引用：李磊, 谢峰. 关于时间慢变的广义Logistic模型的多尺度分析[J]. 应用数学进展, 2018, 7(7): 956-961. https://doi.org/10.12677/AAM.2018.77112

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